1. Field of the Invention
The present invention relates to a simulator for an integrated circuit. More particularly, the present invention relates to a method for extrapolating worst-case Simulation Program with Integrated Circuit Emphasis (SPICE) model parameters for an integrated circuit.
2. Description of the Related Art
When designing integrated circuits, most designers easily verify whether a designed circuit is capable of operating and meeting desired specifications through simulations using a representative circuit simulator such as SPICE. Moreover, as SPICE becomes more readily applied to devices having high speed and large scale, simulation of complete systems, including all designed circuits becomes simplified. Therefore, in addition to the electrical specifications of a designed circuit, recently, dispersion characteristics, which may appear in a manufactured integrated circuit, have been estimated and controlled as well.
SPICE is a program that solves equivalent equations representing the electrical characteristics of a unit device taking into consideration the number of devices used and the electrical connections among the devices. The reliability of SPICE simulation results depends on the accuracy of values of model parameters (or process parameters) included in the equivalent equations and the values of various coefficients. Accordingly, to perform a precise and estimable simulation, accurate model parameters of unit devices to be integrated on a semiconductor wafer should be provided in advance.
In extrapolating SPICE model parameters, initially, a plurality of devices are manufactured using appropriate processes. Many devices are selected from among the manufactured devices and their electrical characteristics are measured. Statistical data reflecting the electrical characteristics is prepared. Then, model parameters and coefficients of a SPICE simulator are set such that simulation results are the same as the previously prepared statistical data when devices having the same conditions (dose of a donor or acceptor, size of a transistor, thickness of silicon dioxide, resistance per one square unit, dielectric constant, and the like) as those of the manufactured devices are modeled. For example, SPICE model coefficients are set by fitting to a voltage-current characteristic curve according to a ratio of gate width to gate length of devices used during relevant processes.
Usually, as described above, model parameters may be obtained using the voltage-current characteristic curve of a device, and the reliability of a simulator is satisfactory. However, when simulating a complete system including all designed circuits as well as individual unit devices, dispersion characteristics and relationships between the individual devices and the complete system must be taken into account. In order to perform such a statistical simulation, it is necessary to provide a set of worst-case SPICE model parameters such as the threshold voltage Vth and saturation current Idsat of a device.
FIG. 1 is a flowchart of a conventional method for extrapolating SPICE model parameters. Referring to FIG. 1, the method includes manufacturing semiconductor devices in step 100; measuring typical data, worst-case data, and best-case electrical characteristic data of the manufactured devices in step 101; extrapolating model parameters using the typical data measured in step 101 in step 102; determining whether the model parameters extrapolated in step 102 satisfy predetermined specifications in step 103 and executing step 102 if it is determined that the model parameters do not satisfy the specifications; determining a set of typical SPICE model parameters in step 104 if it is determined that the extrapolated model parameters satisfy the specifications in step 103; selecting key parameters using the worst-case data and typical data measured in step 101 in step 105; calculating initial values and input variables in step 106; calculating an objective function using the key parameters, initial values, and input variables in step 107; calculating input variables that change according to the results of the calculation performed in step 107 in step 108; determining whether the input variables obtained as the result of the calculation performed in step 108 meet the specifications in step 109 and executing step 105 or 106 after optimizing the key parameters in step 110, if it is determined that the input variables do not meet the specifications; and determining a set of worst-case SPICE model parameters in step 111 if it is determined that the input variables meet the specifications in step 109.
The conventional method described above requires step 105 of selecting key parameters and step 110 of optimizing the key parameters in order to determine a set of worst-case SPICE model parameters. These two steps 105 and 110 require significant processing time. Moreover, the conventional method has a limit to fitting worst-case model parameters to the worst-case electrical characteristics of a key device.